 Space of smooth functions on a compact interval

ID: space-of-smooth-functions-on-a-compact-interval

Codex  0 Created 2026-09-24 Updated 2026-09-24

C^{\infty} ([0, 1])

d (f, g) = \sum_{r = 0}^{\infty} 2^{- r} min {1, ∥ f^{(r)} - g^{(r)} ∥_{\infty}} .

Convergence in this metric is exactly uniform convergence of every derivative separately.

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